What is 4log_{b}(x)+1/2 log_{b}(y)-3log_{b}(2z) ?

The solution to 4log_{b}(x)+1/2 log_{b}(y)-3log_{b}(2z) is log_{b}((x^4y^{1/2})/(8z^3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4log_{b}(x)+1/2 log_{b}(y)-3log_{b}(2z)

simplify

4 lo g_{b} (x) + \frac{1}{2} lo g_{b} (y) - 3 lo g_{b} (2 z)

lo g_{b} (\frac{x ^{4} y ^{\frac{1}{2}}}{8 z ^{3}})

Solution steps

4 lo g_{b} (x) + \frac{1}{2} lo g_{b} (y) - 3 lo g_{b} (2 z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 lo g_{b} (x) = lo g_{b} (x^{4})

= lo g_{b} (x^{4}) + \frac{1}{2} lo g_{b} (y) - 3 lo g_{b} (2 z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} lo g_{b} (y) = lo g_{b} (y^{\frac{1}{2}})

= lo g_{b} (x^{4}) + lo g_{b} (y^{\frac{1}{2}}) - 3 lo g_{b} (2 z)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{b} (x^{4}) + lo g_{b} (y^{\frac{1}{2}}) = lo g_{b} (x^{4} y^{\frac{1}{2}})

= lo g_{b} (x^{4} y^{\frac{1}{2}}) - 3 lo g_{b} (2 z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{b} (2 z) = lo g_{b} ((2 z)^{3})

= lo g_{b} (x^{4} y^{\frac{1}{2}}) - lo g_{b} ((2 z)^{3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{b} (x^{4} y^{\frac{1}{2}}) - lo g_{b} ((2 z)^{3}) = lo g_{b} (\frac{x ^{4} y ^{\frac{1}{2}}}{( 2 z ) ^{3}})

= lo g_{b} (\frac{x ^{4} y ^{\frac{1}{2}}}{( 2 z ) ^{3}})

Simplify

\frac{x ^{4} y ^{\frac{1}{2}}}{( 2 z ) ^{3}} : \frac{x ^{4} y ^{\frac{1}{2}}}{8 z ^{3}}

= lo g_{b} (\frac{x ^{4} y ^{\frac{1}{2}}}{8 z ^{3}})

lo g_{a} (\frac{3 ^{4}}{4 ^{2} a ^{7}})

ln (x^{\frac{1}{2}} y^{9}) - ln (z^{4})

ln (x) + ln (y) - 5 ln (z)

ln ((x + 3)^{3}) - 2 ln (x) - 2 ln (x^{2} + 3 x)

lo g_{10} (7 x^{4})

What is 4log_{b}(x)+1/2 log_{b}(y)-3log_{b}(2z) ?
The solution to 4log_{b}(x)+1/2 log_{b}(y)-3log_{b}(2z) is log_{b}((x^4y^{1/2})/(8z^3))